Comparison of Artificial Neural Networks with Partial Least Squares Regression for Simultaneous Determinations by ICP-AES

Simultaneous determination of several elements （U, Ta, Mn, Zr and W） with inductively coupled plasma atomic emission spectrometry （ICP-AES） in the presence of spectral interference was performed using chemometrics methods. True comparison between artificial neural network （ANN） and partial least squares regression （PLS） for simultaneous determination in different degrees of overlap was investigated. The emission spectra were recorded at uranium analytical line （263.553 nm） with a 0.06 nm spectral window by ICP-AES. Principal component analysis was applied to data and scores on 5 dominant principal components were subjected to ANN. A 5-5-5 （input, hidden and output neurons） network was used with linear transfer function after both hidden and output layers. The PI,S model was trained with five latent variables and 20 samples in calibration set. The relative errors of predictions （REP） in test set were 3.75% and 3.56% for ANN and PLS respectively.     

Quantitative determination of ethanol in heated plumes by passive Fourier transform infrared remote sensing measurements

Quantitative calibration models are developed for passive Fourier transform infrared (FT-IR) remote sensing measurements of open-air-generated vapors of ethanol. These experiments serve as a feasibility study for the use of passive FT-IR measurements in quantitative determinations of industrial stack emissions. A controlled-temperature plume generator is used to produce plumes of known concentrations of pure ethanol and mixtures of ethanol and methanol. Analyte plumes are generated over the path-averaged concentration range of 20-300 ppm-m and stack temperatures of 125, 150, 175, and 200 degrees C. A novel experimental setup is employed in which an ambient temperature polyvinyl chloride backdrop is placed behind the emission stack and used as a target for the passive IR measurements. An emission FT-IR spectrometer with telescope entrance optics is then employed to view the generated plumes against the backdrop. Signal processing techniques based on signal averaging and bandpass digital filtering are applied to both interferogram and single-beam spectral data obtained from these measurements, and the resulting filtered signals are used as inputs into the generation of multivariate partial least-squares (PLS) calibration models. Successful calibration models are obtained with both interferogram and spectral data, and neither analysis requires the collection of separate IR background data. For a set of validation data collected on a different day from the calibration measurements, standard errors of prediction of 30.6 and 32.2 ppm-m ethanol are obtained for the PLS models based on interferogram and spectral data, respectively.     

Partial least-squares with residual bilinearization for the spectrofluorimetric determination of pesticides. A solution of the problems of inner-filter effects and matrix interferents

This paper demonstrates for the first time the power of a chemometric second-order algorithm for predicting, in a simple way and using spectrofluorimetric data, the concentration of analytes in the presence of both the inner-filter effect and unsuspected species. The simultaneous determination of the systemic fungicides carbendazim and thiabendazole was achieved and employed for the discussion of the scopes of the applied second-order chemometric tools: parallel factor analysis (PARAFAC) and partial least-squares with residual bilinearization (PLS/RBL). The chemometric study was performed using fluorescence excitation-emission matrices obtained after the extraction of the analytes over a C18-membrane surface. The ability of PLS/RBL to recognize and overcome the significant changes produced by thiabendazole in both the excitation and emission spectra of carbendazim is demonstrated. The high performance of the selected PLS/RBL method was established with the determination of both pesticides in artificial and real samples.     

Resolution of ternary mixtures of salicylic, salicyluric and gentisic acids by partial least squares and principal component regression: Optimization of the scanning path in the excitation-emission matrices

The resolution of ternary mixtures of salicylic, salicyluric and gentisic acids has been accomplished by partial least squares (PLS) and principal component regression (PCR) multivariate calibration. The total luminescence information of the compounds has been used to optimize the spectral data set to perform the calibration. A comparison between the predictive ability of the three multivariate calibration methods, PLS-1, PLS-2 and PCR, on three spectral data sets, excitation, emission and synchronous spectra, has been performed. The excitation spectrum has been the best scanning path for salicylic and salicyluric acid determinations, while the emission spectrum has been the best for the gentisic acid determination. The convenience of analysing the total luminescence spectrum information when using multivariate calibration methods on fluorescence data is demonstrated.     

Laser-induced breakdown spectrometry in jewellery industry. Part II: quantitative characterisation of goldfilled interface

A new application of laser-induced breakdown spectrometry (LIBS) and multivariate data analysis, namely partial least-squares regression (PLS) in the jewellery industry is reported. The method was designed for the quantitative characterisation of the interface of goldfilled, a material widely used in costume jewellery fabrication, by monitoring the emission lines of the elements present in the sample, while subjecting the piece to a number of laser pulses. The method also provides quantitative information about the composition of a given layer of the material of a special interest at the interface in order to know the existence of diffusion phenomena.     

用于癌症病人初级临床诊断的化学计量学研究

用感应耦合等离子体原子发射光谱及石墨炉原子吸收测定了正常人及癌症病人头发与血清样品中13个元素。将所得数据送入计算机, 分别用化学计量学中PLS及Gram-Schmidt多元分析方法处理了血清与头发样本。在两种情况下均得到了病人与正常人分类极其清晰的二维判别图。头发样本的判别失误率低于血清样本。头发样品取样、存储及运输容易, 也宜于进行光谱分析, 因此可将头发用作癌症初级临床诊断中的分析样品。     

Evaluation of smoothing techniques in the run to run optimization of fed‐batch processes with u‐PLS

Run to run (R2R) optimization based on unfolded Partial Least Squares (u‐PLS) is a promising approach for improving the performance of batch and fed‐batch processes as it is able to continuously adapt to changing processing conditions. Using this technique, the regression coefficients of PLS are used to modify the input profile of the process in order to optimize the yield. When this approach was initially proposed, it was observed that the optimization performed better when PLS was combined with a smoothing technique, in particular a sliding window filtering, which constrained the regression coefficients to be smooth. In the present paper, this result is further investigated and some modifications to the original approach are proposed. Also, the suitability of different smoothing techniques in combination with PLS is studied for both end‐of‐batch quality prediction and R2R optimization. The smoothing techniques considered in this paper include the original filtering approach, the introduction of smoothing constraints in the PLS calibration (Penalized PLS), and the use of functional analysis (Functional PLS). Two fed‐batch process simulators are used to illustrate the results. Copyright © 2015 John Wiley & Sons, Ltd.     

PLS works

In a recent paper, claims were made that most current implementations of PLS provide wrong and misleading residuals [1]. In this paper the relation between PLS and Lanczos bidiagonalization is described and it is shown that there is a good rationale behind current implementations of PLS. Most importantly, the residuals determined in current implementations of PLS are independent of the scores used for predicting the dependent variable(s). Oppositely, in the newly suggested approach, the residuals are correlated to the scores and hence may be high due to variation that is actually used for predicting. It is concluded that the current practice of calculating residuals be maintained. Copyright © 2008 John Wiley & Sons, Ltd.     

Resolution of mixtures of three nonsteroidal anti-inflammatory drugs by fluorescence using partial least squares multivariate calibration with previous wavelength selection by Kohonen artificial neural networks

A spectrofluorometric method for the quantitative determination of flufenamic, mefenamic and meclofenamic acids in mixtures has been developed by recording emission fluorescence spectra between 370 and 550 nm with an excitation wavelength of 352 nm. The excitation–emission spectra of these compounds are deeply overlapped which does not allow their direct determination without previous separation. The proposed method applies partial least squares (PLS) multivariate calibration to the resolution of this mixture using a set of wavelengths previously selected by Kohonen artificial neural networks (K-ANN). The linear calibration graphs used to construct the calibration matrix were selected in the ranges from 0.25 to 1.00 μg ml⁻¹ for flufenamic and meclofenamic acids, and from 1.00 to 4.00 μg ml⁻¹ for mefenamic acid. A cross-validation procedure was used to select the number of factors. The selected calibration model has been applied to the determination of these compounds in synthetic mixtures and pharmaceutical formulations.     

A Complementary Metal Oxide Semiconductor sensor array based detection system for Laser Induced Breakdown Spectroscopy: Evaluation of calibration strategies and application for manganese determination in steel

This paper describes a low cost detection system for Laser Induced Breakdown Spectroscopy based on a simple spectrograph employing a conventional diffraction grating and a non-intensified, non-gated, non-cooled 1024 pixel Complementary Metal Oxide Semiconductor linear sensor array covering the spectral range from about 250 to 390 nm. It was employed in conjunction with a 1064 nm, 5 ns pulse duration Nd:YAG laser source for analyzing steel samples using the integration of 300 analysis pulses (35 mJ each). That led to gains in the signal-to-noise ratio of approximately 3 and 16 for Mn and Fe peaks, respectively, in addition to gains in the emission intensities of about 5.3, both in comparison with the integration of just 50 analysis pulses. The acquired emission spectra were used for Mn determination, in the range from 0.214 to 0.608% m/m as previously determined by ICP OES, evaluating different univariate (at different discrete wavelengths) and multivariate (over different spectral ranges) calibration strategies. The best results, using a PLS calibration model in the spectral range from 292.9 to 294.5 nm (related to Mn emission peaks), had relative errors of prediction of the Mn concentrations, for samples not employed in the calibration, from 0.3 to 7.3%, which are similar to or better than those obtained for Mn determination in steel using higher cost detection systems. The successful analytical application of the new detection system demonstrated that the performance of low cost detection systems can be very good for specific applications and that its low resolution and sensitivity can be at least partially compensated by the use of chemometrics and the integration of analysis pulses.     

偏最小二乘回归用于近红外光谱分析的稳健策略

偏最小二乘法（PLS）在近红外光谱（NIR）定量分析中占有重要地位,但预测结果往往容易受到样本分组和奇异样本等因素的影响,稳健性不强。多模型PLS (EPLS）方法在模型稳健性上得到提高,然而它无法识别样本中存在的奇异样本。为了同时提高模型的预测准确性和稳健性,本文提出了一种根据取样概率重新取样的多模型PLS方法,称为稳健共识PLS（RE-PLS）方法。该方法通过迭代赋权偏最小二乘法(IRPLS)计算样本回归残差得到每个校正集样本的取样概率,然后根据样本的取样概率来选择训练子集建立多个PLS模型,最后将所有PLS模型的预测结果平均作为最终预测结果。该方法用于两种不同植物样品的近红外光谱建模,并与传统的PLS及EPLS方法进行比较。结果表明该方法可以有效的避免校正集中奇异样本对模型的影响,同时可以提高预测精确度和稳健性。对于含有较多奇异样本的,复杂近红外光谱烟草实际样本,利用简单PLS或者EPLS方法建模预测效果不是很理想,而RE-PLS凭借其独特优势则有望在这种复杂光谱定量分析中得到广泛的应用。     

Partitioned partial least squares regression with application to a batch fermentation process

The performance of Partial Least Squares regression (PLS) in predicting the output with multivariate cross‐ and autocorrelated data is studied. With many correlated predictors of varying importance PLS does not always predict well and we propose a modified algorithm, Partitioned Partial Least Squares (PPLS). In PPLS the predictors are partitioned into smaller subgroups and the important subgroups with high prediction power are identified. Finally, regular PLS analysis using only those subgroups is performed. The proposed Partitioned PLS (PPLS) algorithm is used in the analysis of data from a real pharmaceutical batch fermentation process for which the process variables follow certain profiles during a specific fermentation period. We observed that PPLS leads to a more accurate prediction of the yield of the fermentation process and an easier interpretation, since fewer predictors are used in the final PLS prediction. In the application important issues such as alignment of the profiles from one batch to another and standardization of the predictors are also addressed. For instance, in PPLS noise magnification due to standardization does not seem to create problems as it might in regular PLS. Finally, PPLS is compared to several recently proposed functional PLS and PCR methods and a genetic algorithm for variable selection. More specifically for a couple of publicly available data sets with near infrared spectra it is shown that overall PPLS has lower cross‐validated error than PLS, PCR and the functional modifications hereof, and is similar in performance to a more complex genetic algorithm. Copyright © 2011 John Wiley & Sons, Ltd.     

A probabilistic derivation of the partial least-squares algorithm

Traditionally the partial least-squares (PLS) algorithm, commonly used in chemistry for ill-conditioned multivariate linear regression, has been derived (motivated) and presented in terms of data matrices. In this work the PLS algorithm is derived probabilistically in terms of stochastic variables where sample estimates calculated using data matrices are employed at the end. The derivation, which offers a probabilistic motivation to each step of the PLS algorithm, is performed for the general multiresponse case and without reference to any latent variable model of the response variable and also without any so-called "inner relation". On the basis of the derivation, some theoretical issues of the PLS algorithm are briefly considered: the complexity of the original motivation of PLS regression which involves an "inner relation"; the original motivation behind the prediction stage of the PLS algorithm; the relationship between uncorrelated and orthogonal latent variables; the limited possibilities to make natural interpretations of the latent variables extracted.     

Sample-distance partial least squares: PLS optimized for many variables,with application to CoMFA

Summary Three-dimensional molecular modeling can provide an unlimited number m of structural properties. Comparative Molecular Field Analysis (CoMFA), for example, may calculate thousands of field values for each model structure. When m is large, partial least squares (PLS) is the statistical method of choice for fitting and predicting biological responses. Yet PLS is usually implemented in a property-based fashion which is optimal only for small m. We describe here a sample-based formulation of PLS which can be used to fit any single response (bioactivity). SAMPLS reduces all explanatory data to the pairwise distances among n sample (molecules), or equivalently to an n-by-n covariance matrix C. This matrix, unmodified, can be used to fit all PLS components. Furthermore, SAMPLS will validate the model by modern resampling techniques, at a cost independent of m. We have implemented SAMPLS as a Fortran program and have reproduced conventional and cross-validated PLS analyses of data from two published studies. Full (leaveach-out) cross-validation of a typical CoMFA takes 0.2 CPU s. SAMPLS is thus ideally suited to structure-activity analysis based on CoMFA fields or bonded topology. The sample-distance formulation also relates PLS to methods like cluster analysis and nonlinear mapping, and shows how drastically PLS simplifies the information in CoMFA fields.Abbreviations PLS partial least squares - SAMPLS sample-distance partial least squares - CoMFA comparative molecular field analysis.     

Simultaneous fluorometric determination of nalidixic acid and 7-hydroxymethylnalidixic acid by partial least squares calibration

The resolution of binary mixtures of nalidixic acid (NA) and 7-hydroxymethylnalidixic acid (OH-NA) has been accomplished by partial least squares (PLS) and principal component regression (PCR) multivariate calibration. The method of determination is based on the fluorescence emission of these compounds in the presence of gamma-cyclodextrin (gamma-CD). The formation of the inclusion compounds gives rise to an increase of the fluorescence emission compared to aqueous solution. The total luminescence information of the compounds has been used to optimize the spectral data set to perform the calibration. A comparison between the predictive ability of three multivariate calibration methods, PLS-1, PLS-2 and PCR, on three spectral data sets, excitation, emission and synchronous spectra has been performed. The PLS-1 method, applied to the emission spectra, has been selected as optimum. The proposed method has been applied to the simultaneous determination of NA and OH-NA in urine. Recovery values from urine samples containing (NA) and (OH-NA) range from 91 to 103% (mean 97%), and from 92 to 105% (mean 99%), respectively.     

Orthogonal projection to latent structures solution properties for chemometrics and systems biology data

Partial least squares (PLS) is a widely used algorithm in the field of chemometrics. In calibration studies, a PLS variant called orthogonal projection to latent structures (O‐PLS) has been shown to successfully reduce the number of model components while maintaining good prediction accuracy, although no theoretical analysis exists demonstrating its applicability in this context. Using a discrete formulation of the linear mixture model known as Beer's law, we explicitly analyze O‐PLS solution properties for calibration data. We find that, in the absence of noise and for large n, O‐PLS solutions are simpler but just as accurate as PLS solutions for systems in which analyte and background concentrations are uncorrelated. However, the same is not true for the most general chemometric data in which correlations between the analyte and background concentrations are nonzero and pure profiles overlap. On the contrary, forcing the removal of orthogonal components may actually degrade interpretability of the model. This situation can also arise when the data are noisy and n is small, because O‐PLS may identify and model the noise as orthogonal when it is statistically uncorrelated with the analytes. For the types of data arising from systems biology studies, in which the number of response variables may be much greater than the number of observations, we show that O‐PLS is unlikely to discover orthogonal variation whether or not it exists. In this case, O‐PLS and PLS solutions are the same. Copyright © 2011 John Wiley & Sons, Ltd.     

Multivariate methods on the excitation emission matrix fluorescence spectroscopic data of diesel-kerosene mixtures: a comparative study

Quantitative determination of kerosene fraction present in diesel has been carried out based on excitation emission matrix fluorescence (EEMF) along with parallel factor analysis (PARAFAC) and N-way partial least squares regression (N-PLS). EEMF is a simple, sensitive and nondestructive method suitable for the analysis of multifluorophoric mixtures. Calibration models consisting of varying compositions of diesel and kerosene were constructed and their validation was carried out using leave-one-out cross validation method. The accuracy of the model was evaluated through the root mean square error of prediction (RMSEP) for the PARAFAC, N-PLS and unfold PLS methods. N-PLS was found to be a better method compared to PARAFAC and unfold PLS method because of its low RMSEP values.     

Regression with multiple regressor arrays

Extension of standard regression to the case of multiple regressor arrays is given via the Kronecker product. The method is illustrated using ordinary least squares regression (OLS) as well as the latent variable (LV) methods principal component regression (PCR) and partial least squares regression (PLS). Denoting the method applied to PLS as mrPLS, the latter was shown to explain as much or more variance for the first LV relative to the comparable L‐partial least squares regression (L‐PLS) model. The same relationship holds when mrPLS is compared to PLS or n‐way partial least squares (N‐PLS) and the response array is 2‐way or 3‐way, respectively, where the regressor array corresponding to the first mode of the response array is 2‐way and the second mode regressor array is an identity matrix. In a comparison with N‐PLS using fragrance data, mrPLS proved superior in a validation sense when model selection was used. Though the focus is on 2‐way regressor arrays, the method can be applied to n‐way regressors via N‐PLS. Copyright © 2007 John Wiley & Sons, Ltd.